Optimizing a Constraint: Reconstructing an Integer Programming Constraint More Simply

Objectives

The first objective is to minimize the absolute value of the new right-hand side:

\[ \Variable{Objective1} = |\Argument{a[0]}| \cdot \Variable{Scale[0]} \]

The second objective is to minimize the sum of absolute values of the new left-hand side coefficients:

\[ \Variable{Objective2} = \sum _{j \in \text {VARS}} |\Argument{a[j]}| \cdot \Variable{Scale[j]} \]